Problem: Simplify the following expression: $\dfrac{40p}{70p^3}$ You can assume $p \neq 0$.
$ \dfrac{40p}{70p^3} = \dfrac{40}{70} \cdot \dfrac{p}{p^3} $ To simplify $\frac{40}{70}$ , find the greatest common factor (GCD) of $40$ and $70$ $40 = 2 \cdot 2 \cdot 2 \cdot 5$ $70 = 2 \cdot 5 \cdot 7$ $ \mbox{GCD}(40, 70) = 2 \cdot 5 = 10 $ $ \dfrac{40}{70} \cdot \dfrac{p}{p^3} = \dfrac{10 \cdot 4}{10 \cdot 7} \cdot \dfrac{p}{p^3} $ $\phantom{ \dfrac{40}{70} \cdot \dfrac{1}{3}} = \dfrac{4}{7} \cdot \dfrac{p}{p^3} $ $ \dfrac{p}{p^3} = \dfrac{p}{p \cdot p \cdot p} = \dfrac{1}{p^2} $ $ \dfrac{4}{7} \cdot \dfrac{1}{p^2} = \dfrac{4}{7p^2} $